BurstMon test with stationary noise



h50 trends for stationary noise

Conditions:
     The plot shows h50 calculated by BurstMon (blue line) for stationary white noise substituted instead of ADC channel data. The initial approximation for h50 named amp0 calculated by BurstMon from noise estimation is shown by magenta line. In case of stationary noise both lines must show constant values with some variations due to stochastic nature of input signal and finite accuracy of detection modeling. The h50 series plotted above has relative RMS (Root-Mean-Square) 3.2%. This is achieved using 500 total number of injections per time stride 60 seconds. To calculate h50 BurstMon computed Least Square fit of 5 measurements of detection efficiency at 5 different injection amplitudes at each time stride 60 sec. Fitting function was sigmoid, eff=1/(1+(h/h50)^gamma). RMS for obtained series of h50 matches the 3.2 % average error calculated from Least Square fit. The relative RMS of initial approximation is 0.66%, i.e. about 5 times smaller. The lower RMS value arises from the larger number of data points accounted by amp0. While amp0 accounts for all data in frequency range of particular waveform, the value of h50 effectively sences data only within close vicinity in time to injection points, this accounts for 0.008 sec * 500 injections = 4 seconds of data from whole stride of  60 seconds long. This should lead to the difference of sqrt(60/4)~ 4 times in resulting RMS. Despite amp0 has smaller RMS the calculation of amp0 doesn't take into account all details of the detection process so it could not be used as good estimation of h50. The amp0 is the first approximation of value of  h50 and it is used by BurstMon to choose initial injection amplitudes close to 50% detection efficiency.